Simplify the following expression: $ a = \dfrac{-4p + 6}{5p - 1} - \dfrac{-6}{5} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-4p + 6}{5p - 1} \times \dfrac{5}{5} = \dfrac{-20p + 30}{25p - 5} $ Multiply the second expression by $\dfrac{5p - 1}{5p - 1}$ $ \dfrac{-6}{5} \times \dfrac{5p - 1}{5p - 1} = \dfrac{-30p + 6}{25p - 5} $ Therefore $ a = \dfrac{-20p + 30}{25p - 5} - \dfrac{-30p + 6}{25p - 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-20p + 30 - (-30p + 6) }{25p - 5} $ Distribute the negative sign: $a = \dfrac{-20p + 30 + 30p - 6}{25p - 5}$ $a = \dfrac{10p + 24}{25p - 5}$